Building Math Fluency

     I’ve had a couple conversations about how kids learn math facts recently. I thought I would share how I helped my kids develop math fluency and share some resources you can use to help your child strengthen his or her math fluency.   To better understand the approach I take to learning math facts and building fluency, I recommend reading the following article, Fluency Without Fear by mathematics education professor Dr. Jo Boaler.

The child first makes a representation a number using the number puzzles.  Then she describes and labels the shape with an equation.  The number puzzles and equations cards are found in Developing Number Concepts by Kathy Richardson.


     When I was a math coach in Boston, I had the opportunity to work with very knowledgeable math teachers and specialists.  I learned how children develop mathematical understandings and build fluency.  This background helped me understand that children need a variety of experiences with numbers to develop number sense. Number sense is having a “deep understanding of numbers and the ways they relate to each other” (Jo Boaler).  Children need to have lots of opportunities to count, represent and talk about numbers.  These experiences with number serve as the basis for learning math facts, not memorization. 

We cannot rush our children through these important experiences; rather, we must give them the time they need to build this foundation”    – Kathy Richardson

Spielgaben Wood Toys

     At home, math is a natural part of our day.  Since the kids were little, part of their toy collection included puzzles, blocks and shapes like the ones in the picture above.  As the children got older, we began to do mental math and oral story problems during dinner or car rides.  The kids have grown up enjoying math because it has always been a playful part of their day.  We never use flash cards and I never challenge them to see how fast they can solve a problem.

 Building Fluency with School Aged Children

  • Math Talks is an activity described in Fluency Without Fear that can help your child build fluency and number sense. The idea is to solve a computation problem mentally.  For example solve 15+ 23= ___.  Each person solves the problem then shares how they solved it.  You can start with simple problems and move to more complex ones as the children get older.  You can do any of the operations and include fractions and decimals for older students.
  • Snap It is another activity to help children learn addition combinations.  This activity requires snap cubes or unifix cubes.                          IMG_4934
  • Use flash cards to write or tell a story problem to go with the equation.
  • Use flash cards to model the problem using counters or toys such as, toy cars, minifigs, or rocks.

Older children who are learning about multiplication benefit from similar games and activities but they focus on representing groups.

  • How Close to 100?  You will need two dice and the handout to play this game.  The dice tell you the dimensions of the array to make on the grid.  Take turns rolling the dice and recording the arrays.  Try to fill the grid as much as possible.
  • Math Cards Instead of traditional flash cards, use various representations of multiplication to practice multiplication pairs.

On the site you can print out math cards to practice this way.

Math Cards from from Click the link above for the printable.
  • Use flash cards to write or tell a story problem to go with the equation.
  • Use flash cards to model the problem using counters or small toys.

There are more games and activities on the site that you can play with your child or use in your classroom.

Once a child is given the opportunity to develop his concept of number relationships and understands that numbers can be taken apart and put together, they will have a more efficient way of learning their math facts.  Children who use their math facts to solve problems, use the relationships between numbers to solve unknown facts.

If you are a stickler for using flashing cards, here is a Math Facts Mat printable I created to help your child sort math combinations and record ways to learn unknown math facts by relating them to known facts.

Building Fluency_ Math

For example, to learn 5+6 = 11, a child may think, “I know 5+5=10 and 6 is one more than 5, so 5+6 must be 11.” 

Building Fluency_ Math (1)

I hope this has been helpful.


Published by

Maria Arana

Hi, I am Maria, a mom to three wonderful kiddos. My family and I live in Phoenix, Arizona. We love the beauty of the desert southwest. I am a former primary teacher and elementary math coach. I love to encourage my children to follow their interests and passions. At Guided Learning Studio, I offer private personalized lessons and enrichment classes. Tutoring services are best for families seeking long-term educational support over a semester or school-year.

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